Linear Algebra: Theory, Intuition, Code

by Mike X. Cohen

Linear algebra is perhaps the most important branch of mathematics for computational sciences, including machine learning, AI, data science, statistics, simulations, computer graphics, multivariate analyses, matrix decompositions, signal processing, and so on.
The way linear algebra is presented in traditional textbooks is different from how professionals use linear algebra in computers to solve real-world applications in machine learning, data science, statistics, and signal processing. For example, the "determinant" of a matrix is important for linear algebra theory, but should you actually use the determinant in practical applications? The answer may surprise you!
If you are interested in learning the mathematical concepts linear algebra and matrix analysis, but also want to apply those concepts to data analyses on computers (e.g., statistics or signal processing), then this book is for you. You'll see all the math concepts implemented in MATLAB and in Python.

Unique aspects of this
- Clear and comprehensible explanations of concepts and theories in linear algebra.
- Several distinct explanations of the same ideas, which is a proven technique for learning.
- Visualization using graphs, which strengthens the geometric intuition of linear algebra.
- Implementations in MATLAB and Python. Com'on, in the real world, you never solve math problems by hand! You need to know how to implement math in software!
- Beginner to intermediate topics, including vectors, matrix multiplications, least-squares projections, eigendecomposition, and singular-value decomposition.
- Strong focus on modern applications-oriented aspects of linear algebra and matrix analysis.
- Intuitive visual explanations of diagonalization, eigenvalues and eigenvectors, and singular value decomposition.
- Codes (MATLAB and Python) are provided to help you understand and apply linear algebra concepts on computers.
- ALL CODE IS DOWNLOADABLE from
- A combination of hand-solved exercises and more advanced code challenges. Math is not a spectator sport!

Genres: Mathematics, Programming, Software

589 pages, Paperback

Published February 1, 2021

Reviews

[Amir V · Rating 4 out of 5]

The Good:

Connecting many linear algebra concepts to their code implementations. Honestly the documentation for the np.linalg module might be a compelling linear algebra study blueprint in and out of itself.
Intuitive explanations and just the right amount of humor throughout the text. Some of the proofs are very nicely explained.


The not so good:

The visualizations could be better.
The leaning into MATLAB/Python code could be much more dramatic and might have given this book its own special identity among a plethora of introductory linear algebra books.

[Dinghao Luo · Rating 5 out of 5]

Like Mike X Cohen’s videos, the book moves from simple to advanced, starting with vectors and dimensionality and ending with PCA. The code challenges at the end of each chapter are especially useful, reinforcing the material extremely well. It’s also the only linear algebra textbook I’ve seen so far that explains four different ways to compute matrix multiplication (and provides proofs for them).

[Aaron · Rating 5 out of 5]

Gor good use of this book for simple computations